Here you can see my curriculum vitae.
Among others, I am interested in the following research topics:
The potentialities of statistical physics to face the multi-scale complex system description have already been shown. Thus for example, Kolmogorov and Oboukhov on their papers from 1941 and 1962 developed a statistical theory showing the multi-scale behavior of turbulence and the existence of an energy cascade from large to small scales. This statistical framework was later generalized under the name of Multifractal Theory 21 and used to describe multi-scale couplings in a vast range of complex systems such as: fluid turbulence, climate or neural signals. Indeed, this multi-scale behavior can be frequently modelled by scale invariant processes, which are commonly used in physics to describe phase transitions. On the other hand, in 1948 Shannon developed Information Theory (IT), which is a theoretical viewpoint aiming at statistically describing the mathematical laws governing the transmission, storage, processing, measurement and representation of information. Thus, the amount of information needed to completely characterize the probability density function of a process or system provides a measure of its complexity. In the last years, the advantages of Information Theory in the study of complex systems are being highlighted, especially because of its power to characterize non-linear behaviors and interactions. However, complex systems are most of the time multi-scale, and consequently this Information Theory framework should be adapted to characterize relationships and interactions among scales. Thus, I first showed that the multi-scale entropy rate describes the distribution of information across scales [1], and that the distance from Gaussianity accross scales characterizes intermittency (multifractality) [2], both in turbulent velocity measures. Second, I showed the advantages of such a framework over classical Fourier or multifractal analysis [3]. Moreover, I generalized this multi-scale Information Theory framework to analyse the scale-invariance properties of non-stationnary processes with stationary increments [4] and to quantify non-stationarity [5]. I recently adapted the framework to deal with multidimensional tensors and I studied images of isotropic and anisotropic turbulent flows from Direct Numerical Simulations [6]. However, this framework should be still enhanced to provide a full characterization of scale-invariance and to probe more complex scale interactions such as causal ones.
I am specially interested in the development of physics-infused neural network models to synthesize 1-dimensional stochastic fields with turbulent velocity statistics. I already developed two models grounding on the Kolmogorov-Obukhov theories of turbulence. The first model only imposes on the generated field the Kolmogorov-Obukhov laws for second, third and fourth order structure functions [1]. This model is trained without data and is able to correctly recover the imposed statistics but fails when recovering higher-order ones. The second model is a multicriteria and multiscale Generative Adversarial Network, which, in addition to impose the Kolmogorov-Obukhov laws for second, third and fourth order structure functions, includes a training criterion comparing the entropy of experimental and generated turbulent velocity fields [2]. So, this model tries to mimick the full probability density function of the velocity field. Among the future perspectives, I consider to generalize these models to generate 2D and 3D stochastic fields with turbulent statistics as well as conditioning the models by the Reynolds number of the flow to be generated.
Wiener-Granger causality states that a process X causes another process Y if the prediction of future values of Y using the previous samples of both processes X and Y is more succesful than the prediction of future values of Y using only previous samples of Y. Transfer entropy and related IT tools such as Directed Information are measures of non-linear Wiener-Granger causality between time series, and have been frequently interpreted as a measure of information flows. Then, the question naturally arises, do information flows between scales of complex systems exist? or, at least, are there Wiener causality relationships between different scales of complex systems? This problem involve two difficulties: first finding a correct definition of information flows and causality relationships in the studied system, and second, an adapted definition of scale allowing the measuring and interpretation of information flows across scales. A first study on information flows between scales in turbulence can be found in chapter 8 of my PhD thesis.
Each fluid particle of the ocean surface is characterized by some features: salt and nutrient contents, heat, particulate matter such as plankton and marine debris etc. Lagrangian ocean analysis is based on the description of Lagrangian trajectories of fluid particles in the ocean surface, and aims at mapping the seawater motion between ocean regions as well as the transport of the fluid particle features. Thus, the characterization and modelling of Lagrangian ocean surface dynamics is a major issue in oceanographic and climate research, with applications in weather forecasting, search and rescue operations, iceberg tracking, and marine ecology (monitoring of fish larvae or pollutants) among others. Today, surface drifting buoys provide experimental in-situ measures of ocean surface velocities. These drifters behave as Lagrangian fluid particles following trajectories governed by both small and large scale dynamics. Furthermore, different kinds of numerical models have been developed to describe ocean dynamics and can be then used to forecasting activities. However, these models are also based on different physical hypothesis that lead to different performances depending on the scales of the motion. Thus, the simulated and observed dynamics present very often different statistical behaviors, leading to poor agreements between them. Grounded on Artificial Intelligence, we aim at better describe Lagrangian dynamics at sea surface, and so to provide improved versions of numerical lagrangian particles simulations [1].
Together with researchers from INRAe Bordeaux, CESBIO Toulouse, CNRM Toulouse, Universidad de Valencia and ONERA Toulouse, I am involved in two projects focused on the development of image processing methodologies for the study of urban environments from remote sensing data. The first part of the project aims at developing empirical, physical and data-based models for temperature unmixing from multi-spectral satellite imagery and their applications in the study of urban heat islands [1] [2] [3] [4] [5]. The second part of the project aims at developing new methodologies for monitoring the health status of urban vegetation from satellite data [6] [7].
Together with researchers from Ifremer, CNRM, LAERO Toulouse, CECI Toulouse, CNRS, ENS from Lyon and IMT Atlantique, I develop new image processing methodologies for the study of the marine-atmospheric boundary layer from remote sensing data. These methodologies ground on multi-scale decompositions combined with second and high-order statistical moments. We focus on the study of the imprint of turbulent dynamical structures such as convective rolls and cells on the sea surface roughness as observed by Synthetic Aperture Radar imagery [1] [2].
Turbulencia y multifractalidad ochenta años después de la teoría de Kolmogorov 1941. Revista Española de Física, vol 35, num 1, pag 15-19, Enero-marzo 2021.